Subcritical Sevastyanov branching processes with nonhomogeneous Poisson immigration

We consider a class of Sevastyanov branching processes with nonhomogeneous Poisson immigration. These processes relax the assumption required by the Bellman–Harris process which imposes the lifespan and offspring of each individual to be independent. They find applications in studies of the dynamics...

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Bibliographic Details
Published inJournal of applied probability Vol. 54; no. 2; pp. 569 - 587
Main Authors Hyrien, Ollivier, Mitov, Kosto V., Yanev, Nikolay M.
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.06.2017
Applied Probability Trust
Subjects
Asymptotic properties
Immigration
Random variables
Research Papers
Theorems
Branching process
immigration
60J85
62P10
Secondary 60F05
Primary 60J80
Poisson process
limit theorem
Immigration
Limit theorems
Branching processes
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Summary:We consider a class of Sevastyanov branching processes with nonhomogeneous Poisson immigration. These processes relax the assumption required by the Bellman–Harris process which imposes the lifespan and offspring of each individual to be independent. They find applications in studies of the dynamics of cell populations. In this paper we focus on the subcritical case and examine asymptotic properties of the process. We establish limit theorems, which generalize classical results due to Sevastyanov and others. Our key findings include a novel law of large numbers and a central limit theorem which emerge from the nonhomogeneity of the immigration process.
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Postal address: Department of Operations Research, Probability and Statistics, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria, yanev@math.bas.bg
Postal address: Faculty of Aviation, National Military University “Vasil Levski”, 5856 D. Mitropolia, Pleven, Bulgaria kmitov@yahoo.com
Postal address: Department of Biostatistics and Computational Biology, University of Rochester, Rochester, NY 14642, USA Ollivier Hyrien@urmc.rochester.edu
ISSN:0021-9002
1475-6072
DOI:10.1017/jpr.2017.18